Shallow Reinforced Concrete Foundations

his article presents an overview of the • For use in load combination 7: design requirements for shallow reinforced E = Eh - Ev = ρQE - 0.2SDS D Structural concrete foundations (spread footings and In these equations, ρ is the redundancy factor Tmat foundations) supporting buildings assigned to determined in accordance with ASCE/SEI 12.3.4, Seismic Design Category (SDC) D, E, or F. Also SDS is the design spectral response acceleration at Design included is a proposed design method that goes short periods, and QE are the effects due to the beyond requirements in current codes and stan- horizontal seismic forces. dards. Although the following discussion focuses The combined factored stresses at the base of the design issues for exclusively on spread footings supporting mem- footing must be less than or equal to the design structural engineers bers of the seismic-force-resisting system (SFRS), soil bearing strength, ϕQns. The resistance factor,ϕ , it is also applicable to mat foundations. is given in ASCE/SEI Table 12.13-1 and is equal According to ASCE/SEI 7-16, Minimum Design to 0.45 for bearing strength. ASCE/SEI 12.13.5.2 Loads and Associated Criteria for Buildings and permits ϕ to be taken as 0.80 where the nominal Other Structures, Section 12.18.9.2, buildings are bearing strength has been determined by in-situ permitted to be supported on shallow foundations testing of prototype foundations when the test- provided the foundations are designed and detailed ing program has been® approved by the authority in accordance with ASCE/SEI 12.13.9.2.1 and the having jurisdiction. conditions of ASCE/SEI 12.13.9.2 are met. The nominal soil bearing strength, Qns, is per- mitted to be determined by the following methods: • Presumptive load-bearing values Shallow Reinforced ConcreteCopyright Foundations (organic silts, organic clays, peat, or non-engineered fill are assumed not to have a presumptive load capacity). Design for SDC D, E, Determining Base Area • Geotechnical site investigations by a registered and F Buildings design professional, which include field and Bearing failure is the primary design consideration laboratory testing. when footings are subjected to seismic forces. • In-situ testing of prototype foundations. By David A. Fanella, Ph.D., S.E., It is common practice to use service load com- P.E., F.ACI, F.ASCE, and binations to size the footing with an allowable Michael Mota, Ph.D., P.E., bearing capacity that is equal to the static bearing SECB, F.ASCE, F.ACI, F.SEI capacity multiplied by a factor to account for the transient naturemagazine of the earthquake forces. The S T2018 InternationalR U Building CodeC (IBC), T Section U R E 1806.1, permits the presumptive vertical and lat- eral bearing pressures values in Table 1806.2 to be increased by one-third where the alternative basic load combinations of IBC 1605.3.2 that include earthquake forces are used. It is also permitted David A. Fanella is Senior in such cases to use allowable bearing capacities Director of Engineering at the that have been determined from a geotechnical Concrete Reinforcing Steel investigation. Institute and can be reached ASCE/SEI 12.13 contains requirements for at [email protected]. the design of foundations, including spread footings. In lieu of performing a linear analysis Michael Mota is Vice President that includes foundation flexibility and the load- of Engineering at the Concrete deformation characteristics of the foundation soil Reinforcing Steel Institute and can system (ASCE/SEI 12.13.3), the base dimensions be reached at [email protected]. of a footing can be determined utilizing either a strength design method (ASCE/SEI 12.13.5) or an allowable stress design method (ASCE/ SEI 12.13.6). Strength Design Method In the strength design method, load combinations 1 through 7 in ASCE/SEI 2.3.1 and 2.3.6 are used with the seismic load effects, E, determined in accordance with ASCE/SEI 12.4.2: • For use in load combination 6: Figure 1. Soil pressure distributions beneath a footing E=Eh + Ev = ρQE + 0.2SDS D subjected to axial force and bending moment.

38 March 2018 with ASCE/SEI 12.13.4 for foundations of strength, ϕQns. The area of the footing is buildings where (1) the structure is designed in determined based on the governing load com- accordance with the Equivalent Lateral Force bination and the appropriate equation for Procedure (ELFP) in ASCE/SEI 12.8 and (2) maximum factored bearing stress. the structure is not an inverted pendulum Allowable Stress Method or cantilevered column type structure. Only the seismic load effects may be reduced by In the allowable stress design method, load 25% when calculating the bearing pressures; combinations 1 through 10 in ASCE/SEI all other load effects must not be reduced. 2.4.1 and 2.4.5 are used with the seismic A 10% decrease of the overturning effects is load effects, E, calculated in accordance with permitted when a modal analysis in accordance ASCE/SEI 12.4.2 to determine the maximum with ASCE/SEI 12.9 is performed. bearing stresses at the base of a footing, which Analysis of bearing stresses using the strength must be less than or equal to the allowable design method depends on whether inelastic bearing capacity. As in the case of the strength soil response is acceptable or not. If elastic design method, reduction of foundation over- response is required, the maximum factored turning effects ®is permitted in accordance with bearing stress is calculated using the appropri- ASCE/SEI 12.13.4. ate elastic equations in Figure 1 where factored Proposed Design Method axial forces, Pu, and bending moments, Mu, are determined by load combinations 1 The earthquake effects, E, determined in through 7 in ASCE/SEI 2.3.1 and 2.3.6. accordance with ASCE/SEI Chapter 12 are Where inelasticCopyright soil response is accept- less than those that would be expected during able, the maximum bearing stress, which is a design-level earthquake. Therefore, in the assumed to be constant over the entire contact case of footings, the reactions caused by E that Figure 2. Soil pressure distribution beneath a area, can be calculated assuming full plasticity are transferred from the supported member footing assuming full inelastic soil response. of the soil (Figure 2). to the footing will typically be smaller than qu,max = Pu /BL´ those that would be transferred during an According to ASCE/SEI 12.13.5, overturn- Regardless of elastic or inelastic soil response, actual seismic event. Thus, determining the ing effects at the soil-foundation interface are the maximum bearing stress, qu,max, must be bearing stresses (and the required flexural and permitted to be reduced by 25% in accordance less than or equal to the design soil bearing shear strengths) based on code-prescribed S T RADVERTISEMENT–Formagazine U Advertiser Information,C visit www.STRUCTUREmag.orgT U R E

STRUCTURE magazine39 March 2018 earthquake forces inherently implies that Design Procedure report, times the density of the soil. IBC some inelastic behavior is allowed in the foot- Table 1806.2 provides presumptive passive ing regardless if strength-level or service-level The following design procedure can be used pressure values in pounds-per-square-foot- load combinations are used. Allowing such to size the base area of a footing supporting per-foot-below-grade for various soil types. inelastic behavior may be tolerable for typical members that are part of the SFRS in build- The lateral resistance provided by friction is buildings assigned to nonessential risk cat- ings assigned to SDC D, E, or F: equal to the total normal force at the base of egories (ASCE/SEI Table 1.5-1). However, 1) Determine the factored load effects using the footing times an ultimate coefficient of foundations that are designed in this way may load combinations 1 through 7 in ASCE/ friction. When determining the total normal possibly be damaged during a seismic event, SEI 2.3.1 and 2.3.6, where load combina- force, load combination 7 should be used and may not perform as intended during tions 6 and 7 include seismic load effect because this results in the smallest normal subsequent seismic events. Furthermore, with overstrength. force at the base. Ultimate coefficients of fric- inspecting foundations after an earthquake 2) Where elastic soil response is required, tion depend on the soil type and are generally can be very expensive or might not even be determine the base area of the footing, reported in a geotechnical report. possible, so there is usually no direct way of Af, using the appropriate elastic equations ASCE/SEI 12.13.5.1.1 permits the total ascertaining if damage has occurred unless in Figure 1 and the design soil bearing design lateral strength, ϕQns, to be the sum of ® the damage is obvious. Repairing founda- strength, ϕQns. the values determined for passive pressure and tions is also costly and, in some cases, may 3) Where inelastic soil response is permitted, horizontal sliding (from friction, cohesion, or not be feasible. determine the base area of the footing, some combination thereof). The geotechnical For buildings assigned to SDC D, E, and F, it Af, using the uniform bearing pressure report should specifically designate what type is recommended to design footings using load distribution illustrated in Figure 2 and or types of horizontal sliding resistance are combinations 1 through 7 in ASCE/SEI 2.3.1 the design soil bearing strength, ϕQns. applicable at a site. Copyright and 2.3.6, where load combinations 6 and 7 Allowable Stress Design Method include seismic load effect with overstrength: Resistance to Lateral Loads • Load combination 6: 1.2D + Ev + In the allowable stress design method, allow- Emh + L + 0.2S = (1.2 + 0.2SDS)D + In general, lateral forces from earthquakes are able passive bearing pressures and coefficients ΩoQE + L + 0.2S transferred from a footing to the adjoining of friction are used in conjunction with • Load combination 7: 0.9D - Ev + Emh soil through friction at the base of the footing maximum seismic load effects calculated by = (0.9 - 0.2SDS ) + ΩoQE and passive bearing pressure along the edge of allowable stress load combinations to deter- In these equations, Ωo is the overstrength the footing perpendicular to the direction of mine whether resistance to lateral sliding is factor given in ASCE/SEI Table 12.2-1 for analysis (Figure 3). As in the case of bearing adequate or not. As in the case of bearing the SFRS. pressure at the base of a footing, both strength pressure at the base of a footing, allowable pas- Like the design of collectors in accordance design and allowable stress design methods sive pressures may be increased when seismic with current provisions, footings are antici- canmagazine be used to check if resistance to sliding load combinations are considered to account pated to respond primarily inS the elastic T range Ris adequate U or not. C T Ufor transientR loadE effects. when designed using this approach, thereby Strength Design Method Design and Detailing Requirements reducing the likelihood of damage when sub- jected to a design-level seismic event. Nonlinear In the strength design method, factored The applicable design and detailing require- response is limited to the supported mem- lateral forces must be less than or equal to ments given in ACI Chapter 13 and ACI bers, which are correctly detailed according the design lateral strength, ϕQns. The reduc- 18.13.2 must be satisfied for footings sup- to the appropriate requirements in ACI 318- tion factor, ϕ, is given in ASCE/SEI Table porting members of the SFRS in buildings 14, Building Code Requirements for Structural 12.13-1, and is equal to 0.50 for lateral assigned to SDC D through F. Similar to the Concrete, Chapter 18. As an upper limit, the resistance provided by passive bearing pres- cases of determining the base area of a foot- forces delivered to a footing need not exceed sure and 0.85 for lateral resistance provided ing and checking for sliding resistance, it is the capacity of the supported structure. by sliding (either friction or cohesion). recommended that reinforcement for flexure ACI 12.13.5.1.1 contains and force transfer at the interface are deter- the types of soils that pro- mined using load combinations 1 through vide lateral sliding resistance 7 in ASCE/SEI 2.3.1 and 2.3.6, where load from friction and cohesion. combinations 6 and 7 include seismic load Values of Qns, based on the effect with overstrength. Shear strength soil profile at the site, are requirements should be satisfied based on typically provided in the those load combinations as well. geotechnical report. Additional in-depth information and Passive bearing pressure worked-out design examples can be found varies linearly with respect in the CRSI publication Design and Detailing to the depth below grade. At of Low-Rise Reinforced Concrete Buildings.▪ a depth ds below grade, the passive pressure is equal to ds times the passive pressure coef- The online version of this article ficient, Kp, which is typically contains references. Please visit Figure 3. Lateral load transfer by friction and passive bearing stress. provided in a geotechnical www.STRUCTUREmag.org.

STRUCTURE magazine40 March 2018 References ACI (American Concrete Institute). 2014. Building Code Requirements for Structural Concrete and Commentary. ACI 318-14, Farmington Hills, Michigan. ASCE (American Society of Civil Engineers). 2017. Minimum Design Loads and Associated Criteria for Buildings and Other Structures. ASCE/SEI 7-16, Reston, VA. CRSI (Concrete Reinforcing Steel Institute). 2017. Design and Detailing of Low-Rise Reinforced Concrete Buildings. Schaumburg, IL. ICC (International Code Council). 2017. International Building Code. Washington, D.C.

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STRUCTURE magazine41 March 2018